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Preserving differential privacy has been well studied under the centralized setting. However, it’s very challenging to preserve differential privacy under multiparty setting, especially for the vertically partitioned case. In this work, we propose a new framework for differential privacy preserving multiparty learning in the vertically partitioned setting. Our core idea is based on the functional mechanism that achieves differential privacy of the released model by adding noise to the objective function. We show the server can simply dissect the objective function into single-party and cross-party sub-functions, and allocate computation and perturbation of their polynomial coefficients t o l ocal p arties. Our method n eeds o nly o ne r ound of noise addition and secure aggregation. The released model in our framework achieves the same utility as applying the functional mechanism in the centralized setting. Evaluation on real-world and synthetic datasets for linear and logistic regressions shows the effectiveness of our proposed method. 

In differentially private stochastic gradient descent (DPSGD), gradient clipping and random noise addition disproportionately affect underrepresented and complex classes and subgroups. As a consequence, DPSGD has disparate impact: the accuracy of a model trained using DPSGD tends to decrease more on these classes and subgroups vs. the original, non-private model. If the original model is unfair in the sense that its accuracy is not the same across all subgroups, DPSGD exacerbates this unfairness. In this work, we study the inequality in utility loss due to differential privacy, which compares the changes in prediction accuracy w.r.t. each group between the private model and the non-private model. We analyze the cost of privacy w.r.t. each group and explain how the group sample size along with other factors is related to the privacy impact on group accuracy. Furthermore, we propose a modified DPSGD algorithm, called DPSGD-F, to achieve differential privacy, equal costs of differential privacy, and good utility. DPSGD-F adaptively adjusts the contribution of samples in a group depending on the group clipping bias such that differential privacy has no disparate impact on group accuracy. Our experimental evaluation shows the effectiveness of our removal algorithm on achieving equal costs of differential privacy with satisfactory utility.